Here is the full list of all 35 Battle Royale Tycoon achievements.
Entertain Mr America
Complete Scenario 3
Entertain the Ogre
$100,000 in the Bank
Receive $500,000
Achieve Park Rating 90
Play 100 Months
VIP left with 80 Happiness
Build Arena Team Deathmatch
Build Every Arena Type
Build all Fun Buildings
Unlock all Research
Complete Scenario 2
Achieve Park Rating 60
Build Arena King of the Hill
Build Arena Capture The Flag
Use a Steam Workshop item
Buy 100 Weapons
Place 50 Environment Objects
Hire 50 Workers
Complete Scenario 1
Entertain 5 VIPs
Entertain the Spartan
500 Guests Visited Total
Entertain Spandex Man
Clean Up 100 Trash
Build Arena Battle Royale
Entertain Blueprint Man
100 Guests in Park
Entertain a VIP
Entertain 1000 Guests
Entertain TF2 Medic
Build Arena Defuse
Build ATM
Build Arena Duel